{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:BJDCUVDDVVPV7XDEKKEHZF3K2V","short_pith_number":"pith:BJDCUVDD","canonical_record":{"source":{"id":"0910.5444","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-10-28T17:44:04Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"d0f77eddb86978e25b88b59bd4ad2f3b5706ed4adbb21f395efb7a391d958897","abstract_canon_sha256":"1461a7280834b1b4f34f2c676d2b0f97ee606fe01329969815ac0744cffdd9a9"},"schema_version":"1.0"},"canonical_sha256":"0a462a5463ad5f5fdc6452887c976ad5785e3fbb6a7dd7564de248ea4b7e5dbe","source":{"kind":"arxiv","id":"0910.5444","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.5444","created_at":"2026-05-18T03:44:58Z"},{"alias_kind":"arxiv_version","alias_value":"0910.5444v2","created_at":"2026-05-18T03:44:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.5444","created_at":"2026-05-18T03:44:58Z"},{"alias_kind":"pith_short_12","alias_value":"BJDCUVDDVVPV","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"BJDCUVDDVVPV7XDE","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"BJDCUVDD","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:BJDCUVDDVVPV7XDEKKEHZF3K2V","target":"record","payload":{"canonical_record":{"source":{"id":"0910.5444","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-10-28T17:44:04Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"d0f77eddb86978e25b88b59bd4ad2f3b5706ed4adbb21f395efb7a391d958897","abstract_canon_sha256":"1461a7280834b1b4f34f2c676d2b0f97ee606fe01329969815ac0744cffdd9a9"},"schema_version":"1.0"},"canonical_sha256":"0a462a5463ad5f5fdc6452887c976ad5785e3fbb6a7dd7564de248ea4b7e5dbe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:58.019257Z","signature_b64":"RXHn2Mzf/SCaA7g6hyuogR49JE1OnbD7hVD2gNQ9rTzQHmL7kksgEggAek7d8SGW0/o7tD9RAdbWaGu0/mG2DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a462a5463ad5f5fdc6452887c976ad5785e3fbb6a7dd7564de248ea4b7e5dbe","last_reissued_at":"2026-05-18T03:44:58.018572Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:58.018572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0910.5444","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:44:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ush/sUQIMQL7BHIPMYFh/2Z8Vbx5w1M9/x2wH9L7yQZBlZAKZCXjVS1GiNGe+l73H8qul1pYdRwGgv/sKXAECQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T05:35:02.130570Z"},"content_sha256":"7a872dfb3a3d2900bdb76d70af42f94423c819458f6d9fd6825a1b4cce78cfcb","schema_version":"1.0","event_id":"sha256:7a872dfb3a3d2900bdb76d70af42f94423c819458f6d9fd6825a1b4cce78cfcb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:BJDCUVDDVVPV7XDEKKEHZF3K2V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dismantlability of weakly systolic complexes and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Damian Osajda, Victor Chepoi","submitted_at":"2009-10-28T17:44:04Z","abstract_excerpt":"The main goal of this paper is proving the fixed point theorem for finite groups acting on weakly systolic complexes. As corollaries we obtain results concerning classifying spaces for the family of finite subgroups of weakly systolic groups and conjugacy classes of finite subgroups. As immediate consequences we get new results on systolic complexes and groups. The fixed point theorem is proved by using a graph-theoretical tool - dismantlability. In particular we show that 1-skeleta of weakly systolic complexes, i.e. weakly bridged graphs, are dismantlable. On the way we show numerous characte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.5444","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:44:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iJEYUXUn87W4SqcsM0tyT28FMpf/3ySKz7IR7b3H3dYPU+Q3dKNGvnEWzmOdbdUy714FAt5PQsLwghZZv8aWCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T05:35:02.131234Z"},"content_sha256":"a9be44cfec55ec15181171257fc150816f60b71674f84dc71d4578331954a954","schema_version":"1.0","event_id":"sha256:a9be44cfec55ec15181171257fc150816f60b71674f84dc71d4578331954a954"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BJDCUVDDVVPV7XDEKKEHZF3K2V/bundle.json","state_url":"https://pith.science/pith/BJDCUVDDVVPV7XDEKKEHZF3K2V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BJDCUVDDVVPV7XDEKKEHZF3K2V/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T05:35:02Z","links":{"resolver":"https://pith.science/pith/BJDCUVDDVVPV7XDEKKEHZF3K2V","bundle":"https://pith.science/pith/BJDCUVDDVVPV7XDEKKEHZF3K2V/bundle.json","state":"https://pith.science/pith/BJDCUVDDVVPV7XDEKKEHZF3K2V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BJDCUVDDVVPV7XDEKKEHZF3K2V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:BJDCUVDDVVPV7XDEKKEHZF3K2V","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1461a7280834b1b4f34f2c676d2b0f97ee606fe01329969815ac0744cffdd9a9","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-10-28T17:44:04Z","title_canon_sha256":"d0f77eddb86978e25b88b59bd4ad2f3b5706ed4adbb21f395efb7a391d958897"},"schema_version":"1.0","source":{"id":"0910.5444","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.5444","created_at":"2026-05-18T03:44:58Z"},{"alias_kind":"arxiv_version","alias_value":"0910.5444v2","created_at":"2026-05-18T03:44:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.5444","created_at":"2026-05-18T03:44:58Z"},{"alias_kind":"pith_short_12","alias_value":"BJDCUVDDVVPV","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"BJDCUVDDVVPV7XDE","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"BJDCUVDD","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:a9be44cfec55ec15181171257fc150816f60b71674f84dc71d4578331954a954","target":"graph","created_at":"2026-05-18T03:44:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The main goal of this paper is proving the fixed point theorem for finite groups acting on weakly systolic complexes. As corollaries we obtain results concerning classifying spaces for the family of finite subgroups of weakly systolic groups and conjugacy classes of finite subgroups. As immediate consequences we get new results on systolic complexes and groups. The fixed point theorem is proved by using a graph-theoretical tool - dismantlability. In particular we show that 1-skeleta of weakly systolic complexes, i.e. weakly bridged graphs, are dismantlable. On the way we show numerous characte","authors_text":"Damian Osajda, Victor Chepoi","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-10-28T17:44:04Z","title":"Dismantlability of weakly systolic complexes and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.5444","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7a872dfb3a3d2900bdb76d70af42f94423c819458f6d9fd6825a1b4cce78cfcb","target":"record","created_at":"2026-05-18T03:44:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1461a7280834b1b4f34f2c676d2b0f97ee606fe01329969815ac0744cffdd9a9","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-10-28T17:44:04Z","title_canon_sha256":"d0f77eddb86978e25b88b59bd4ad2f3b5706ed4adbb21f395efb7a391d958897"},"schema_version":"1.0","source":{"id":"0910.5444","kind":"arxiv","version":2}},"canonical_sha256":"0a462a5463ad5f5fdc6452887c976ad5785e3fbb6a7dd7564de248ea4b7e5dbe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a462a5463ad5f5fdc6452887c976ad5785e3fbb6a7dd7564de248ea4b7e5dbe","first_computed_at":"2026-05-18T03:44:58.018572Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:58.018572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RXHn2Mzf/SCaA7g6hyuogR49JE1OnbD7hVD2gNQ9rTzQHmL7kksgEggAek7d8SGW0/o7tD9RAdbWaGu0/mG2DA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:58.019257Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.5444","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a872dfb3a3d2900bdb76d70af42f94423c819458f6d9fd6825a1b4cce78cfcb","sha256:a9be44cfec55ec15181171257fc150816f60b71674f84dc71d4578331954a954"],"state_sha256":"4b6a849cdce7311630b8c56858351849a734947d800e7223f20f9abfd8d87a80"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I5cuV9v5csmXlwcL2/QhbcvYfUnkro4bAFshPmlwkcQFhHM2V/S25Uz0fT5fVtYgNkiVt2vt8Z0KWrXsmfWLAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T05:35:02.134768Z","bundle_sha256":"6e4b2f593d49a9ebdae1f71c797f140820d59fcfe3952cba0122fff16a31c7db"}}